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2023-2024 Cowley College Academic Catalog [ARCHIVED CATALOG]

MTH4425 TRIGONOMETRY COURSE PROCEDURE

MTH4425 TRIGONOMETRY

3 Credit Hours

Student Level:  

This course is open to students on the college level in the freshman year.

Catalog Description of the Course

MTH4425 - Trigonometry (3 hrs.)

[KRSN  MAT1030]

Trigonometric functions using the unit circle and right angle trigonometry, graphing applications, analytic trigonometry, vectors, trigonometric complex number applications, parametric and polar equations. This course requires that the students furnish their TI-83 or TI-84PLUS graphing calculator.

Course Classification:

Lecture

Prerequisite:   

A minimum grade of C in MTH 4420 or 23 ACT math score or satisfactory course placement assessment scores.             

Controlling Purpose:  

To provide pre-calculus and physics students with a knowledge of the functions and basic applications of trigonometry.

Core Outcomes:

The learning outcomes and competencies detailed in this course procedure meet, or exceed the learning outcomes and competencies specified by the Kansas Core Outcomes Project for this course, as sanctioned by the Kansas Board of Regents.

Learner Outcomes:  

Students will master the properties of the six basic functions of trigonometry and their inverses through algebraic and graphic analysis, and make applications to geometric measure, mechanics, wavelength, vectors, and complex numbers.

Unit Outcomes for Criterion Based Evaluation:

The following defines the minimum core content not including the final examination period. Instructors may add other content as time allows.

The learning outcomes and competencies detailed in this course meet, or exceed the learning outcomes and competencies specified by the Kansas Core Outcomes Project for this course, as sanctioned by the Kansas Board of Regents.

 

UNIT 1: Trigonometric Functions

Outcomes: The student will be able to describe an angle in both degrees and radians; identify a unit circle and its relationship to real numbers; evaluate trigonometric functions of any angle; use fundamental trigonometric identities; sketch graphs of trigonometric functions; evaluate inverse trigonometric functions and their composition; use trigonometric functions to model and solve real-life problems.

  • Convert between decimals and degrees, minutes, seconds forms for angles.
  • Find the arc length of a circle.
  • Convert from degrees to radians and from radians to degrees.
  • Find the area of a sector of a circle.
  • Find the linear speed of an object traveling in circular motion.
  • Find the exact values of the trigonometric functions using a point on the unit circle.
  • Find the exact values of the trigonometric functions of quadrantal angles.
  • Find the exact values of the trigonometric functions of pi/4 = 45 degrees.
  • Find the exact values of the trigonometric functions of pi/6 = 30 degrees and pi/3 = 60 degrees.
  • Find the exact value of the trigonometric functions for integer multiples of pi/6 = 30 degrees, pi/4 = 45 degrees, and pi/3 = 60 degrees.
  • Use a calculator to approximate the value of a trigonometric function.
  • Use circle of radius r to evaluate the trigonometric functions.
  • Determine the domain and the range of the trigonometric functions
  • Determine the period of the trigonometric functions.
  • Determine the signs of the trigonometric functions in a given quadrant.
  • Find the values of the trigonometric functions using fundamental identities.
  • Find the exact values of the trigonometric functions of an angle given one of the functions and the quadrant of the angle.
  • Use even-odd properties to find the exact values of the trigonometric functions.
  • Graph functions of the form y = A sin (ꞷx) using transformations.
  • Graph functions of the form y = A cos (ꞷx) using transformations.
  • Determine the amplitude and period of sinusoidal functions.
  • Graph sinusoidal functions using key points.
  • Find an equation for a sinusoidal graph.
  • Graph functions of the form y = A tan (ꞷx) + B and y = A cot (ꞷx) + B.
  • Graph functions of the form y = A csc (ꞷx) + B and y = A sec (x) + B.
  • Graph sinusoidal functions: y = A sin (ꞷx - Փ) + B.
  • Find a sinusoidal function from data.

UNIT 2: Analytic Trigonometry

Outcomes: The student will be able to use fundamental trigonometric identities; verify trigonometric identities; solve trigonometric equations; use sum, difference, multiple-angle, and power-reducing, half-angle, product-sum formulas to evaluate trigonometric functions.

  • Find the exact value of the inverse sine, cosine, and tangent functions.
  • Find an approximate value of the inverse sine, cosine, and tangent functions.
  • Use properties of inverse functions to find exact values of certain composite functions.
  • Find the inverse function of a trigonometric function.
  • Solve equations involving inverse trigonometric functions.
  • Find the exact value of expressions involving the arcsin(x), arccos(x), and arctan(x) functions.
  • Know the definition of the arcsec(x), arccsc(x), and arccot(x) functions.
  • Use a calculator to evaluate arcsec(x), arccsc(x), and arccot(x). 
  • Write a trigonometric expression as an algebraic expression.
  • Use algebra to simplify trigonometric expressions.
  • Establish identities.
  • Use sum and difference formulas to find exact values.
  • Use sum and difference formulas to establish identities.
  • Use sum and difference formulas involving inverse trigonometric functions.
  • Use double-angle formulas to find exact values.
  • Use double-angle and half-angle formulas to establish identities.
  • Use half-angle formulas to find exact values.
  • Express products as sums.
  • Express sums as products.
  • Solve equations involving a single trigonometric function.
  • Solve trigonometric equations quadratic in form.
  • Solve trigonometric equations using identities.
  • Solve trigonometric equations linear in sine and cosine.
  • Solve trigonometric equations using a graphing utility.

UNIT 3: Applications of Trigonomectric Functions

Outcomes: The student will be able to use Law of Sines and Law of Cosines; find area of oblique triangles; represent vectors; perform mathematical operations on vectors; find direction of vectors; find dot products of two vectors and use properties of the dot product.

  • Find the value of trigonometric functions of an acute angle using right triangles.
  • Use the complementary angle theorem.
  • Solve right triangles.
  • Solve applied problems.
  • Solve SAA or ASA triangles.
  • Solve SSA triangles.
  • Solve applied problems.
  • Solve SAS triangles.
  • Solve SSS triangles.
  • Solve applied problems.
  • Find the area of SAS triangles.
  • Find the area of SSS triangles.
  • Find an equation for an object in simple harmonic motion.
  • Analyze simple harmonic motion.
  • Analyze an object in damped motion.
  • Graph the sum of two functions

UNIT 4: Polar Coordinates; Vectory

Outcomes: The student should be able to perform operations with complex numbers; find the zeros of a function; multiply and divide complex numbers written in trigonometric form; find powers and nth roots of complex numbers.

  • Plot points using polar coordinates.
  • Convert from polar coordinates to rectangular coordinates.
  • Convert from rectangular coordinates to polar coordinates.
  • Transform equations from polar to rectangular form.
  • Graph and identify polar equations by converting to rectangular equations.
  • Test polar equations for symmetry.
  • Graph polar equations by plotting points.
  • Convert a complex number from rectangular form to polar form.
  • Plot points in the complex plane.
  • Find products and quotients of complex numbers in polar form.
  • Use De Moivre’s Theorem.
  • Find complex roots.
  • Graph vectors.
  • Find a position vector.
  • Add and subtract vectors.
  • Find a scalar multiple and the magnitude of a vector.
  • Find a unit vector.
  • Find a vector from its direction and magnitude.
  • Analyze objects in static equilibrium.
  • Find the dot product of two vectors.
  • Find the angle between two vectors.
  • Determine whether two vectors are parallel.
  • Determine whether two vectors are orthogonal.
  • Decompose a vector into two orthogonal vectors.
  • Compute work.
  • Find the distance between two points in space.
  • Find position vectors in space.
  • Perform operations on vectors in space.
  • Find the dot product.
  • Find the angle between two vectors.
  • Find the direction angles of a vector.
  • Find the cross product of two vectors
  • Know algebraic properties of the cross product.
  • Know geometric properties of the cross product.
  • Find a vector orthogonal to two given vectors.
  • Find the area of a parallelogram.

Projects Required: 

None

Textbook:

Contact Bookstore for current textbook.

Materials/Equipment Required:

This course requires that the student furnish their own TI-83 or TI84 PLUS graphing calculator.

Attendance Policy:

Students should adhere to the attendance policy outlined by the instructor in the course syllabus.

Grading Policy:

A minimum 50% of the course grade shall consist of proctored assessment(s) of which at least 25% of the course grade shall include a comprehensive departmental final exam.

Maximum class size:

Based on classroom occupancy

Course Timeframe: 

The U.S. Department of Education, Higher Learning Commission and the Kansas Board of Regents define credit hour and have specific regulations that the college must follow when developing, teaching and assessing the educational aspects of the college. A credit hour is an amount of work represented in intended learning outcomes and verified by evidence of student achievement that is an institutionally established equivalency that reasonably approximates not less than one hour of classroom or direct faculty instruction and a minimum of two hours of out-of-class student work for approximately fifteen weeks for one semester hour of credit or an equivalent amount of work over a different amount of time. The number of semester hours of credit allowed for each distance education or blended hybrid courses shall be assigned by the college based on the amount of time needed to achieve the same course outcomes in a purely face-to-face format.

Refer to the following policies:

402.00 Academic Code of Conduct

263.00 Student Appeal of Course Grades

403.00 Student Code of Conduct

Disability Services Program:  

Cowley College, in recognition of state and federal laws, will accommodate a student with a documented disability.  If a student has a disability, which may impact work in this class, which requires accommodations, contact the Disability Services Coordinator.  

DISCLAIMER: THIS INFORMATION IS SUBJECT TO CHANGE. FOR THE OFFICIAL COURSE PROCEDURE CONTACT ACADEMIC AFFAIRS.

​(Updated 3/24/22)